Enumerative induction
Pages 131 - 144
Abstract
The paper explains enumerative induction, the confirmation of a law by its positive instances, in ranking theoretic terms. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. And it shows, finally, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus the paper shows that de Finetti's probabilistic representation theorems may be directly transformed into an account of confirmation of possible laws and that enumerative induction is equivalent to such an account.
References
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de Finetti, B. (1937), "La Prévision: Ses Lois Logiques, Ses Sources Subjectives", Annales de l'Institut Henri Poincaré 7. Engl translation: "Foresight: Its Logical Laws, Its Subjective Sources", in: H. E. Kyburg jr., H.E. Smokler (eds.), Studies in Subjective Probability, New York: John Wiley & Sons 1964, pp. 93--158.
[2]
Gärdenfors, P. (1988), Knowledge in Flux, Cambridge, Mass.: MIT Press.
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Hild, M. (t.a.), Introduction to Induction. On the First Principles of Reasoning.
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Humburg, J. (1971), "The Principle of Instantial Relevance", in: R. Carnap, R.C. Jeffrey (eds.), Studies in Inductive Logic and Probability, Vol. I Berkeley: University of California Press. pp. 225--233.
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Lange, M. (2000), Natural Laws in Scientific Practice, Oxford: University Press.
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Lewis, D.K. (1973), Counterfactuals, Oxford: Blackwell.
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Niiniluoto, I. (1972), "Inductive Systematization: Definition and a Critical Survey", Synthese 25, 25--81.
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Popper, K.R. (1934), Logik der Forschung, Wien: Springer.
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Ramsey, F.P. (1929), "General Propositions and Causality", in: F.P. Ramsey, Foundations. Essays in Philosophy, Logic, Mathematics and Economics, ed. by D.H. Mellor, London: Routledge & Kegan Paul 1978, pp. 133--151.
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Spohn, W. (1983), Eine Theorie der Kausalität, unpublished Habilitationsschrift München.
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Spohn, W. (1986), "The Representation of Popper Measures", Topoi 5, 69--74.
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Spohn, W. (1988), "Ordinal Conditional Functions. A Dynamic Theory of Epistemic States", in: W.L. Harper, B. Skyrms (eds.), Causation in Decision, Belief Change, and Statistics, vol. II, Dordrecht: Kluwer, pp. 105--134.
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Spohn, W. (1993), "Causal Laws are Objectifications of Inductive Schemes", in: J.-P. Dubucs (ed.), Philosophy of Probability, Dordrecht: Kluwer, pp. 223--252.
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Published: 20 June 2003
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